How does the Centroid Calculator work?

x̄ = (1/A) ∫ x dA, ȳ = (1/A) ∫ y dA where A = total area Then: For composite shapes: x̄ = Σ(Aᵢ × x̄ᵢ) / ΣAᵢ Then: Centroid location depends on shape symmetry Then: For symmetric shapes, centroid on axis of symmetry.

Can you give an example of how to use the Centroid Calculator?

Example: Input Triangle vertices gives a result of Centroid average.

Is the Centroid Calculator free to use?

Yes — completely free with no registration, download, or subscription required. All calculations happen instantly in your browser.

How accurate is the Centroid Calculator?

Our Centroid Calculator uses verified mathematical formulas and is accurate to multiple decimal places. Results are calculated in real-time using the same methods used by professionals.

Mathematics

Centroid Calculator

Centroid

Vertices (x,y|x,y|...)

Calculates centroid (center of mass) of 2D shape assuming uniform density.

Symbol	Name	Unit	Description
A	(1/A) ∫ y dA where A = total area	—	(1/A) ∫ y dA where A = total area

Difficulty:advanced

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Did You Know?

Pappus's theorem: volume of revolution = area × distance of centroid to axis × 2π.

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Centroid Calculator

Centroid

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